caa a22 4500 386382913 CHVBK 20180307112049.0 cr unu---uuuuu 161130s1989 xx s 000 0 eng 10.1017/S030821050002391X doi S030821050002391X pii (NATIONALLICENCE)cambridge-10.1017/S030821050002391X Dynamic boundary conditions for the Navier-Stokes equations [Elektronische Daten] When a symmetric rigid body performs a rotation in a fluid, the system of governing equations consists of conservation of linear momentum of the fluid and conservation of angular momentum of the rigid body. Since the torque at the interface involves the drag due to the fluid flow, the conservation of angular momentum may be viewed as a boundary condition for the field equations of fluid motion. These equations at the boundary contain a time derivative and thus are of a dynamic nature. The familiar no-slip condition becomes an additional equation in the system which not only governs the fluid motion, but also the motion of the rigid body. The unknown functions in the system of equations are the velocity and pressure fields of the fluid motion and the angular velocity of the rigid body. In this paper we formulate the physical problem for the case of rotation about an axis of symmetry as an abstract ordinary differential equation in two Banach spaces in which the velocity field is the only unknown. To achieve this, a method for the elimination of the pressure field, which also occurs in the boundary condition, is developed. Existence and uniqueness results for the abstract equation are derived with the aid of the theory of B-evolutions and the associated theory of fractional powers of a closed pair of operators. Copyright © Royal Society of Edinburgh 1989 Grobbelaar-Van Dalsen Maríe Department of Mathematics, Applied Mathematics and Astronomy, University of South Africa, P.O. Box 392, Pretoria 0001, South Africa Sauer Niko Faculty of Science, University of Pretoria, Pretoria 0002, South Africa Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 113/1-2(1989), 1-11 0308-2105 113:1-2<1 1989 113 PRM https://doi.org/10.1017/S030821050002391X text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S030821050002391X text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Grobbelaar-Van Dalsen Maríe Department of Mathematics, Applied Mathematics and Astronomy, University of South Africa, P.O. Box 392, Pretoria 0001, South Africa NATIONALLICENCE 700 1- Sauer Niko Faculty of Science, University of Pretoria, Pretoria 0002, South Africa NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 113/1-2(1989), 1-11 0308-2105 113:1-2<1 1989 113 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge